Advertisement

Computationally Perfect Secret Sharing Scheme Based on Error-Correcting Codes

  • Appala Naidu Tentu
  • Prabal Paul
  • V. Ch. Venkaiah
Part of the Communications in Computer and Information Science book series (CCIS, volume 420)

Abstract

In this paper, we propose a secret sharing scheme for compartmented access structure with lower bounds. Construction of the scheme is based on the Maximum Distance Separable (MDS) codes. The proposed scheme is ideal and computationally perfect. By computationally perfect, we mean, an authorized set can always reconstruct the secret in polynomial time whereas for an unauthorized set this is computationally hard. This is in contrast to some of the existing schemes in the literature, in which an authorized set can recover the secret only with certain probability. Also, in our scheme unlike in some of the existing schemes, the size of the ground field need not be extremely large. This scheme is efficient and requires O(mn 3), where n is the number of participants and m is the number of compartments.

Keywords

Compartmented access structure computationally perfect ideal MDS code perfect secret sharing scheme 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Beimel, A., Tassa, T., Weinreb, E.: Characterizing ideal weighted threshold secret sharing. SIAM J. Disc. Math. 22(1), 360–397 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Blakley, G.R.: Safeguarding cryptographic keys. AFIPS 48, 313–317 (1979)Google Scholar
  3. 3.
    Blakley, G.R., Kabatianski, A.: Ideal perfect threshold schemes and MDS codes. ISIT 1995, 488 (1995)Google Scholar
  4. 4.
    Brickell, E.F.: Some ideal secret sharing schemes. J. Comb. Math. Comb. Comput. 9, 105–113 (1989)MathSciNetGoogle Scholar
  5. 5.
    Collins, M.J.: A note on ideal tripartite access structures, manuscript available at http://eprint.iacr.org/2002/193/2002
  6. 6.
    Farràs, O., Martí-Farré, J., Padró, C.: Ideal multipartite secret sharing schemes. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 448–465. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  7. 7.
    Farràs, O., Padró, C., Xing, C., Yang, A.: Natural generalizations of threshold secret sharing. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 610–627. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  8. 8.
    Ghodosi, H., Pieprzyk, J., Safavi-Naini, R.: Secret Sharing in Multilevel and Compartmented Groups. In: Boyd, C., Dawson, E. (eds.) ACISP 1998. LNCS, vol. 1438, pp. 367–378. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  9. 9.
    Herranz, J., Saez, G.: New results on multipartite access structures. IEEE Proc. Inf. Secur. 153, 153–162 (2006)CrossRefGoogle Scholar
  10. 10.
    Pieprzyk, J., Zhang, X.-M.: Ideal threshold schemes from MDS codes. In: Lee, P.J., Lim, C.H. (eds.) ICISC 2002. LNCS, vol. 2587, pp. 253–263. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  11. 11.
    Karnin, E.D., Greene, J.W., Hellman, M.E.: On secret sharing systems. IEEE Trans. Inf. Theory, IT-29, 35–41 (1983)Google Scholar
  12. 12.
    Kaskaloglu, K., Ozbudak, F.: On hierarchical threshold access structures. In: IST Panel Symposium, Tallinn, Estonia (November 2010)Google Scholar
  13. 13.
    McEliece, R.J., Sarwate, D.V.: On sharing secrets and Reed Solomon codes. Communications of the ACM 24, 583–584 (1981)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Ng, S.-L.: Ideal Secret Sharing Schemes with multipartite access structures. IEEE Proc. Commun. 153, 165–168 (2006)CrossRefzbMATHGoogle Scholar
  15. 15.
    Ozadam, H., Ozbudak, F., Saygi, Z.: Secret sharing schemes and linear codes. In: ISC, Ankara, pp. 101–106 (2007)Google Scholar
  16. 16.
    Shamir, A.: How to share a secret. Comm. ACM 22, 612–613 (1979)CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Simmons, G.J.: How to (Really) Share a secret. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 390–448. Springer, Heidelberg (1990)CrossRefGoogle Scholar
  18. 18.
    Naidu, T.A., Paul, P., Venkaiah, V.C.: Ideal and Perfect Hierarchical Secret Sharing Schemes based on MDS codes. In: Proceeding of International Conference on Applied and Computaional Mathematics, Ankara, Turkey, pp. 256–272 (2012)Google Scholar
  19. 19.
    Tentu, A.N., Paul, P., Vadlamudi, C.V.: Conjunctive Hierarchical Secret Sharing Schemes based on MDS codes. In: Lecroq, T., Mouchard, L. (eds.) IWOCA 2013. LNCS, vol. 8288, pp. 463–467. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  20. 20.
    Naidu, T.A., Paul, P., Venkaiah, V.C.: Ideal and Perfect Hierarchical Secret Sharing Schemes based on MDS codes, eprint.iacr.org/2013/189.pdf
  21. 21.
    The Theory of Error-Correcting Codes. Macwilliams, Sloane (1981)Google Scholar
  22. 22.
    Tassa, T.: Hierarchical Threshold Secret Sharing. Journal of Cryptology 20, 237–264 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  23. 23.
    Tassa, T., Dyn, N.: Multipartite Secret Sharing by Bivariate Interpolation. Journal of Cryptology 22, 227–258 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  24. 24.
    Vinod, V., Narayanan, A., Srinathan, K., Pandu Rangan, C., Kim, K.: On the power of computational secret sharing. In: Johansson, T., Maitra, S. (eds.) INDOCRYPT 2003. LNCS, vol. 2904, pp. 162–176. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  25. 25.
    Yu, Y., Wang, M.: A Probabilistic secret sharing scheme for a compartmented access structure. In: Qing, S., Susilo, W., Wang, G., Liu, D. (eds.) ICICS 2011. LNCS, vol. 7043, pp. 136–142. Springer, Heidelberg (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Appala Naidu Tentu
    • 1
  • Prabal Paul
    • 2
  • V. Ch. Venkaiah
    • 3
  1. 1.CR Rao Advanced Institute of Mathematics, Statistics, and Computer ScienceUniversity of Hyderabad CampusHyderabadIndia
  2. 2.Birla Institute of Technology & ScienceIndia
  3. 3.Department of Computer and Information SciencesUniversity of HyderabadHyderabadIndia

Personalised recommendations